A family of parabolas satisfies the rule y = ax² + 2x + a. a) Express ax² + 2x + a in the form a(x + b)2 + c for real numbers b and c.

b) Give the coordinates of the turning point of the graph of y = ax² + 2x + a in
terms of a

c) For which values of a is ax + 2x + a a perfect square?

d) For which values of a does the graph of y = ax + 2x + a have two x-axis intercepts?​

im alright what do you need

step-by-step explanation:

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form